Title: Looking for Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory – Any modern alternatives?
User: StructEngineer_87 Posted: Today, 11:42 AM
I keep coming across references to the book Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory by Bares (or sometimes attributed to Czerny/Bares). From what I understand, it’s a foundational collection of influence coefficients and closed-form solutions for elastic plates under various loadings and boundary conditions – essentially the pre-FEA handbook.
Does anyone still use this (or have a PDF they could share)? I’m aware it’s long out of print. I’m particularly interested in the diaphragm tables for lateral load distribution in concrete structures.
Also curious – for those who’ve used it, how does it compare to:
Is there any value left in the Bares/Czerny tables beyond academic/historical interest? I’m trying to avoid blindly trusting FEA for preliminary design of unusual slab geometries.
Reply 1 – Senior Member, PE I’ve got a scanned PDF of the Czerny tables (often mis-titled as Bares). The proper reference is usually: Czerny, F. (1976). Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory. Ernst & Sohn.
Be careful – there are two versions: one for slabs (bending moments) and one for diaphragms (in-plane shear/axial stresses). The diaphragm tables are rare.
Key limitations:
Why still useful?
They’re excellent for sanity-checking FEA results, especially for moment coefficients in two-way slabs. I’ve caught many modelling errors (wrong boundary conditions, mesh issues) by comparing mid-span moments to Czerny’s coefficients. Title: Looking for Tables for the Analysis of
Reply 2 – Junior Engineer Why not just use the Eurocode 2 tables for two-way slabs? They’re essentially simplified versions of the same elastic theory.
Reply 1 again – Senior Member, PE Eurocode 2 tables are for ultimate limit state with redistribution. The Czerny tables are purely elastic (serviceability). For example, if you need deflections or crack control in a complex bay, the original elastic coefficients are more accurate. Also, EC2 doesn’t cover irregular shapes or diaphragms.
Reply 3 – Structural Analyst I have a PDF titled “Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory” by Richard Bares (1979, translated from French). It’s ~250 pages. Happy to share a link (mods: is that allowed if it’s out of print/abandoned copyright?).
In terms of modern use:
Honestly, if you do any work with concrete shell roofs or bridge deck slabs, these tables are gold. I keep a printed copy in my office.
OP’s follow-up:
Thanks everyone – especially @Reply3, yes please DM me the PDF link. I’m mainly after the diaphragm tables for a non-rectangular transfer slab. I’ll cross-check with a simple FEA model, but I want the elastic baseline first.
Also, for anyone else looking: I found a partial preview on Google Books, and WorldCat lists it in a few university libraries (signature: TA660.P6 B3713 1979).
Reply 4 – CAE Software User
Worth noting: If you have access to MATLAB or Python, you can generate many of these tables on the fly using Navier’s solution (double Fourier series) for simply supported plates. For clamped edges, Lévy’s method. The Bares tables just saved everyone the computation time in the 1970s.
But for diaphragms (in-plane loading), the governing equation is the Airy stress function – the tables essentially give you coefficients for membrane stresses. Modern FEM is far more flexible. Roark’s Formulas for Stress and Strain (Chapter 11
Final thought from OP:
Sounds like the PDF is worth having for historical reference and quick checks, but don’t rely on it for final design without a sanity check. Thanks all.
If you’d like, I can also summarize the actual content you would find in that PDF (e.g., common coefficient tables for moment and shear).
The seminal work Tables for the Analysis of Plates, Slabs and Diaphragms Based on the Elastic Theory Richard Bareš
is a cornerstone of structural engineering literature. Originally published in German as Berechnungstafeln für Platten und Wandscheiben
, this collection provides a comprehensive set of practical formulas and look-up tables used to solve complex problems in plate and slab analysis without the need for manual, high-level calculus. Overview of the Method The book is built upon the classical elastic theory of plates and shells
, primarily focusing on the linear-elastic behavior of structural elements. Unlike the yield-line theory
, which focuses on collapse loads and plastic behavior, the elastic theory ensures that structural elements remain within their serviceability limits, preventing excessive cracking and deflection.
The analysis typically involves solving the governing differential equations of equilibrium, which can be expressed in terms of bending moments ( cap M sub x cap M sub y ), twisting moments ( cap M sub x y end-sub ), and shear forces ( cap V sub x cap V sub y Fundamental Equations
In elastic theory, the bending of a thin plate is often described by the Lagrange-Euler equation (biharmonic equation): Is there any value left in the Bares/Czerny
nabla squared nabla squared w equals the fraction with numerator q and denominator cap D end-fraction : Deflection of the plate. : Intensity of the distributed load. : Flexural rigidity, defined as Components of the Analysis
Bareš's tables categorize structural elements based on their primary mechanical function and loading:
Based on standard structural engineering literature, the phrase "feature for tables for the analysis of plates slabs and diaphragms based on the elastic theory" most likely refers to the data presentation style found in classic textbooks, specifically the seminal work by S. Timoshenko and S. Woinowsky-Krieger, titled Theory of Plates and Shells.
However, if you are looking for a software feature or a specific PDF document, the interpretation changes slightly.
Here is a detailed breakdown of what this feature entails and where to find the resources.
In remote sites, during power outages, or for freelance engineers without expensive software licenses, a PDF of these tables on a laptop or tablet is an invaluable tool.
In structural engineering terminology:
While their load regimes differ, all three share the need for closed-form or tabulated solutions based on elastic theory. The tables in question often cover:
In the age of finite element software (FEA) like ANSYS, Abaqus, and SAP2000, one might assume that classical hand calculation methods have become obsolete. However, for the discerning structural engineer, the opposite is true. The elastic theory of plates remains the bedrock of structural intuition.
The search for the "Tables for the Analysis of Plates, Slabs, and Diaphragms Based on the Elastic Theory PDF" is not a search for outdated information; it is a search for reliability, speed, and fundamental understanding. These tables, popularized by the seminal work of theorists like Timoshenko, Czerny, and later Bares, provide closed-form solutions to partial differential equations that govern plate bending.
If you are designing reinforced concrete flat slabs, steel floor plates, or shear diaphragms, this resource is indispensable. This article explores where to find these tables, how to interpret them, and why they still outperform software in preliminary design.
